Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc II

In \cite{ds_hfs}, a geometric procedure for constructing a Nevanlinna-Pick problem on $\D^n$ with a specified set of uniqueness was established. In this sequel we conjecture a necessary and a sufficient condition for a Nevanlinna-Pick problem on $\DT$ to have a unique solution. We use the results of \cite{ds_hfs} and Bezout's theorem to establish three special cases of this conjecture.